The above form of GUP is compatible with the modification of uncertainty principle, as proposed in String Theory, DSR, and black hole (BH) physics. For alternate forms of GUP, we refer our readers to Refs. [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]} and for phenomenological implications to Refs. [9]}, [10]}, [11]}, [12]}.
Note that having been derived as a consequence of DSR theories, although the form of GUP as given in Eq. (REF ) is not manifestly Lorentz invariant, it is covariant under the non-linear Lorentz transformations in DSR theories [13]}, [14]}, [15]}, [16]}, [17]}.
The aforementioned forms of the modified commutation relation, namely Eq. (REF ), and of the GUP, namely Eq. (REF ), imply a minimum measurable length and a maximum measurable momentum of the form
\(\Delta x\,\geqslant \,(\Delta x)_{{\rm min}}\, \approx \, \alpha _0\,l_{Pl}\\\nonumber \\\Delta p\,\leqslant \,(\Delta p)_{{\rm max}}\,\approx \,\frac{M_{Pl}\,c}{\alpha _0}~.\) 
